Port-Hamiltonian flexible multibody dynamics
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Port-Hamiltonian flexible multibody dynamics Andrea Brugnoli1 · Daniel Alazard1 · Valérie Pommier-Budinger1 · Denis Matignon1
Received: 10 February 2020 / Accepted: 26 September 2020 © Springer Nature B.V. 2020
Abstract A new formulation for the modular construction of flexible multibody systems is presented. By rearranging the equations for a flexible floating body and introducing the appropriate canonical momenta, the model is recast into a coupled system of ordinary and partial differential equations in port-Hamiltonian (pH) form. This approach relies on a floating frame description and is valid under the assumption of small deformations. This allows including mechanical models that cannot be easily formulated in terms of differential forms. Once a pH model is established, a finite element based method is then introduced to discretize the dynamics in a structure-preserving manner. Thanks to the features of the pH framework, complex multibody systems could be constructed in a modular way. Constraints are imposed at the velocity level, leading to an index 2 quasilinear differential-algebraic system. Numerical tests are carried out to assess the validity of the proposed approach. Keywords Port-Hamiltonian systems · Floating frame formulation · Flexible multibody systems · Structure-preserving discretization · Substructuring
This work is supported by the project ANR-16-CE92-0028, entitled Interconnected Infinite-Dimensional systems for Heterogeneous Media, INFIDHEM, financed by the French National Research Agency (ANR) and the Deutsche Forschungsgemeinschaft (DFG). Further information is available at https://websites.isae-supaero.fr/infidhem/the-project.
B A. Brugnoli
[email protected] D. Alazard [email protected] V. Pommier-Budinger [email protected] D. Matignon [email protected]
1
ISAE-SUPAERO, Université de Toulouse, 10 Avenue Edouard Belin, BP-54032, 31055 Toulouse Cedex 4, France
A. Brugnoli et al.
1 Introduction In structural control codesign of flexible multibody systems, it is especially useful to dispose of a modular description, to simplify analysis. In this spirit, the transfer matrix method [40] and the component mode synthesis [24] are two well-known substructuring techniques that allow the construction of complex multibody systems by interconnecting subcomponents together. A reformulation of the Finite Element-Transfer Matrix (FE-TM) method [47] allows for an easy construction of reduced models that are suited for decentralized control design. For the component mode synthesis, the controlled component synthesis (CCS), a framework for the design of decentralized controller of flexible structures, has been proposed in [49]. Another modeling paradigm based on the component mode synthesis is the two-input twooutput port (TITOP) approach [1]. It conceives the dynamical model of each substructure as a transfer between the accelerations and the external forces at the connection points. This feature allows considering different boundary conditions by inverting specific channels
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